[Paper Review] Toutatis, the Cea-Saclay RFQ code

R. Duperrier, R. Ferdinand+2 more|arXiv (Cornell University)|Aug 17, 2000

Particle accelerators and beam dynamics3 references16 citations

TL;DR

TOUTATIS is a high-precision, multigrid-based RFQ beam dynamics code developed at CEA-Saclay to cross-validate results from PARMTEQM and improve field accuracy in CW high-power linear accelerators. It uses adaptive mesh refinement and a time-stepping algorithm with exact Jacobian preservation to simulate space charge, image effects, and complex vane geometries—including coupling gaps—with sub-5% discrepancy against CERN experiments and 97% transmission in IPHI design tests.

ABSTRACT

A CW high power linear accelerator can only work with very low particles losses and structure activation. At low energy, the RFQ is a very sensitive element to losses. To design the RFQ, a good understanding of the beam dynamics is requested. Generally, the reference code PARMTEQM is enough to design the accelerator. TOUTATIS has been written with goals of cross-checking results and obtaining a more reliable dynamics. This paper relates the different numerical methods used in the code. It is time-based, using multigrids methods and adaptive mesh for a fine description of the forces without being time consuming. The field is accurately calculated through a Poisson solver and the vanes are fully described, allowing to properly simulate the coupling gaps and RFQs extremities. Differences with PARMTEQM and LIDOS.RFQ are shown.

Motivation & Objective

• To develop a reliable, cross-checking alternative to PARMTEQM for RFQ beam dynamics simulations.
• To improve field accuracy in RFQs by fully modeling vane geometry, including coupling gaps and end effects.
• To reduce computation time from days to hours using multigrid methods while maintaining high resolution.
• To enable accurate simulation of complex RFQ geometries such as segmented vane designs with non-uniform gaps.
• To support high-power CW accelerators by minimizing particle losses and structural activation through precise field modeling.

Proposed method

• Employs a time-domain, particle-in-cell (PIC) algorithm with a velocity-dependent leapfrog scheme preserving the Jacobian exactly to avoid artificial emittance growth.
• Uses a 3D finite difference method with weighted coefficients to discretize the Poisson equation, enabling accurate representation of vane boundaries without 'staircase' artifacts.
• Applies multigrid V-cycle relaxation with Gauss-Seidel smoothing, restriction, and prolongation to accelerate convergence of the Poisson solver.
• Implements adaptive mesh refinement (AMR) with a secondary high-resolution grid tuned to the rms bunch size, dynamically adjusting resolution where needed.
• Embeds full vane geometry as Dirichlet boundary conditions in the Poisson solver to model coupling gaps and field distortions accurately.
• Supports PARMTEQM input files directly, enabling seamless migration and validation.

Experimental results

Research questions

• RQ1 How can beam dynamics simulations in RFQs be made more accurate and reliable than with PARMTEQM?
• RQ2 What numerical methods can significantly reduce computation time while maintaining high field resolution in complex RFQ geometries?
• RQ3 How do coupling gaps affect beam transmission and emittance, and how can they be modeled accurately?
• RQ4 Can adaptive mesh refinement improve resolution of space charge effects without prohibitive computational cost?
• RQ5 To what extent can TOUTATIS reproduce experimental measurements compared to existing codes?

Key findings

• TOUTATIS achieves less than 0.7% discrepancy with theoretical fields for 65³ and 33³ grid resolutions, validating its Poisson solver accuracy.
• For the IPHI RFQ design, TOUTATIS simulations show 97% transmission and 12% emittance growth when gaps are at Young’s optimal position, compared to 28% emittance growth when misaligned.
• The code reduces computation time from one week (on a Pentium 450 MHz) to 5 hours using multigrid methods, enabling practical simulation of full RFQs.
• Discrepancy between TOUTATIS and CERN measurements is within 5%, significantly better than PARMULT’s 15% discrepancy.
• Including coupling gaps in simulations is essential—omission leads to overly optimistic predictions of emittance and transmission.
• Adaptive mesh refinement allows high-resolution charge distribution modeling with minimal performance cost, maintaining accuracy during bunch acceleration.